I'm not saying this is the best way...
You can add the feature to kick off jobs remotely using a token. Then you can somehow grab the parameters of the job. For example, if user clicks on job no. 6, then this URL gives you the parameters. With wget/curl magic, I'm sure you can get all the parameters.
http://<jenkins-url>/job/Job-1/6/parameters/
Then you can use the URL pattern below to kick off another job with the parameters gathered above
http://<jenkins-url>/job/myjob/buildWithParameters?token=TOKEN&PARAMETER=Value